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題 名 | Generalized Association Plots: Information Visualization Via Iteratively Generated Correlation Matrices |
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作 者 | Chen,Chun-houh; | 書刊名 | Statistica Sinica |
卷 期 | 12:1 2002.01[民91.01] |
頁 次 | 頁7-29 |
專 輯 | A Special Issue on Bioinformatics |
分類號 | 360.13 |
關鍵詞 | Data visualization; Divisive clustering tree; Latent structure; Perfect symmetry; Proximity matrices; Seriation; |
語 文 | 英文(English) |
英文摘要 | Given a p-dimensional proximity matrix Dp×p, a sequence of correlation matrices, R=(R(1), R(2),…), is iteratively formed from it. Here R(1) is the correlation matrix of the original proximity matrix D and R(n) is the correlation matrix of R(n-1), n>1. This sequence was first introduced by McQuitty (1968), Breiger, Boorman and Arabie (1975) developed an algrotihm, CONCOR, based on their rediscovery of its convergence. The sequence R often converges to a matrix R(∞) whose elements are +1 or -1. This special pattern of R(∞) partitions the p objects into two disjoint groups and so can be recursively applied to generate a divisive hierarchical clustering tree. While convergence is itself useful, we are more concerned with what happens before convergence. Prior to convergence, we note a rank reduction property with elliptical structure: when the rank of R(n) reaches two, the column vectors of R(n) fall on an ellipse in a two-dimensional subspace. The unique order of relative positions for the p points on the ellipse can be used to solve serration problems such as the reordering of a Robinson matrix. A software package, Generalized Association Plots (GAP), is developed which utilizes computer graphics to retrieve important information hidden in the data or proximity matrices. |
本系統中英文摘要資訊取自各篇刊載內容。